Merging Two Faces in L Shape
You can join the boxes by putting in horizontal edges to match across the join, merging vertices, and deleting internal faces.

However, I think you could save yourself quite a lot of trouble by planning ahead, and starting your model entirely in the flat.




Start by cutting edges, putting in loops, where you will eventually need to elevate your walls
To achieve the rounded corners, you may have to E extrude some edges upwards, to make thin walls. With CtrlB you can bevel the vertical edges in the corners you want to be rounded. You can then delete those walls before moving on.
You don't need to worry about quad topology, everything is in flat surfaces, no shading anomalies, this is for printing.
First step, select all the faces and  E extrude to make the floor
Subsequent steps, make selections of faces to extrude upwards to make thick walls, stopping at appropriate heights before reselecting, and extruding again.